Question

The value of $\frac{1}{(216{)}^{-2/3}}+\frac{1}{(256{)}^{-3/4}}+\frac{1}{(32{)}^{-1/5}}$ is:

• A. $102$
• B. $105$
• C. $107$
• D. $109$

Answer 1

The correct option is A $102$

$\frac{1}{(216{)}^{-\frac{2}{3}}}+\frac{1}{(256{)}^{-\frac{3}{4}}}+\frac{1}{(32{)}^{-\frac{1}{5}}}$

$=\frac{1}{(6^3{)}^{-\frac{2}{3}}}+\frac{1}{(4^4{)}^{-\frac{3}{4}}}+\frac{1}{(2^5{)}^{-\frac{1}{5}}}$

$=\frac{1}{6^{-2}}+\frac{1}{4^{-3}}+\frac{1}{2^{-1}}$

$=(6^2+4^3+2^1)$

$=(36+64+2^1)$

$=102$